Question

10 years ago ago Dilip was three times as old as his son and two years hence twice his age will be equal to five times that of his son find their present age​

Answer 1

Looks like that his age becomes 2 times of his son.

Answer:

22 and 46 year.

Step-by-step explanation:

Let ;

      Before 10 years, age of Dilip's son was a and Dilip's age be 3a.  

{ year is ignored in calculation }

     After 2 years( from present ) :

       Age of Dilip = 3a + 10 + 2 = 3a + 12

       Age of Dilip's son = a + 10 + 2 = a + 12

According to the question:

⇒ Age of Dilip = 2 x age of his son

⇒ 3a + 12 = 2( a + 12 )

⇒ 3a + 12 = 2a + 24

⇒ 3a - 2a = 24 - 12

⇒ a = 12

           Hence,  

                Present age of son is a + 10 = 12 + 10 = 22 year

                Present age of Dilip is 3a + 10 = 3( 12 ) + 10 = 46 year

Answer 2

$\huge\sf{Answer:}$

$\underline{\tt Given :}$

➳ Ten years ago ago Dilip was three times as old as his son and two years hence twice his age will be equal to five times that of his son.

$\underline{\tt Find :}$

➳ Find their present age.

$\underline{\tt Calculations :}$

$\underline{\tt According \ to \ the \ question, \ as \ follows:}$

Dividing the cases according to question:

$\tt{Case \ (1):}$

➳ 10 years ago, Dilip was 3 times old as his son.

$\tt{Case \ (2):}$

➳ 2 years he was twice his age will be equal to 5 times the age of his son.

Writing equation according to the above cases as follows:

➳ Let us assume '3x' as age of dilip's age.

➳ Let us assume 'y' as age of dilip's son.

According to case (1):

➳ Well, we know that we have to find their present ages so, calculating afters two years now. Now refers from persent calculating for next 2 years.

$\sf\rightarrow Father's age = 3x + 10 + 2 = 3x + 12$

$\sf\rightarrow Son's age = y + 10 + 2 = y + 12$

According to equation:

➳ Dilips age = 2 times age of his son.

$\sf\rightarrow 3x + 12 = 2 (y + 12)$

$\sf\rightarrow 3x + 12 = 2y + 25$

➳ Well in the second equation we get 2y because in the equation 1 we multiply 2 (×) y + 12.

➳ Well this bracket '(' refers multiplication sign.

$\sf\rightarrow 3x + 12 = 2y + 24$

$\sf\rightarrow 3x - 2y = 24 - 12$

$\sf\rightarrow y = 12$

Therefore, using this above equations we get their ages easily.

➳ (Dilip's age) Father's age = 3x + 10 = 3 × 12 + 10 = (46).

➳ Son's age = 3x + 10 = 12 + 10 = (22).

Therefore 46 and 22 years are their present ages respectively.